SET007 Axioms: SET007+700.ax
%------------------------------------------------------------------------------
% File : SET007+700 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Yet Another Construction of Free Algebra
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : msafree3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 61 ( 1 unt; 0 def)
% Number of atoms : 481 ( 32 equ)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 494 ( 74 ~; 0 |; 215 &)
% ( 15 <=>; 190 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-4 aty)
% Number of functors : 51 ( 51 usr; 3 con; 0-4 aty)
% Number of variables : 217 ( 212 !; 5 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_msafree3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v1_catalg_1(B,A)
& l3_msualg_1(B,A) )
=> ~ v1_xboole_0(k3_card_3(u4_msualg_1(A,B))) ) ).
fof(fc2_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A)
& ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v4_msualg_1(k1_msafree3(A,B),A)
& ~ v1_catalg_1(k1_msafree3(A,B),A) ) ) ).
fof(cc1_msafree3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k1_msafree3(A,B))))
=> ( v1_relat_1(C)
& v1_funct_1(C) ) ) ) ).
fof(cc2_msafree3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k1_msafree3(A,B))))
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v3_trees_2(C)
& v3_trees_9(C)
& v4_trees_9(C) ) ) ) ).
fof(cc3_msafree3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k1_msafree3(A,B))))
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v3_trees_2(C)
& v3_trees_9(C)
& v4_trees_9(C) ) ) ) ).
fof(cc4_msafree3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v3_trees_2(A) )
=> ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v3_trees_2(A) ) ) ).
fof(cc5_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A)
& v1_msualg_6(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_2(C,A,B)
=> v1_msualg_6(C,A) ) ) ).
fof(fc3_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v4_msualg_1(k1_msafree3(A,B),A)
& v2_msafree(k1_msafree3(A,B),A)
& v1_msualg_6(k1_msafree3(A,B),A) ) ) ).
fof(t1_msafree3,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( r1_tarski(A,k1_relat_1(B))
& v2_funct_1(B) )
=> k10_relat_1(B,k9_relat_1(B,A)) = A ) ) ).
fof(t2_msafree3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v1_funcop_1(C)
& m1_pboole(C,A) )
=> ( ( v1_msualg_3(C)
& r2_pboole(A,B,k1_extens_1(A,C)) )
=> r6_pboole(A,k1_equation(A,k14_pboole(A,B,C),C),B) ) ) ) ).
fof(d1_msafree3,axiom,
$true ).
fof(d2_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( ( v4_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ( C = k1_msafree3(A,B)
<=> ? [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))))))
& C = k12_msualg_2(A,k11_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0)))),D)
& r6_pboole(u1_struct_0(A),D,k1_equation(u1_struct_0(A),B,k15_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0)))))) ) ) ) ) ) ).
fof(t3_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(k4_tarski(A,D),u1_struct_0(k5_msafree(B,C)))
<=> r2_hidden(A,k1_funct_1(C,D)) ) ) ) ) ).
fof(t4_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( m1_pboole(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( ( r2_hidden(A,k1_funct_1(D,E))
& r2_hidden(A,k1_funct_1(C,E)) )
<=> r2_hidden(k1_trees_4(k4_tarski(A,E)),k1_funct_1(k1_equation(u1_struct_0(B),D,k15_msafree(B,C)),E)) ) ) ) ) ) ).
fof(t5_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(A,k1_funct_1(C,D))
=> r2_hidden(k1_trees_4(k4_tarski(A,D)),k1_funct_1(u4_msualg_1(B,k1_msafree3(B,C)),D)) ) ) ) ) ).
fof(t6_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( k1_msualg_1(A,C) = k1_xboole_0
=> r2_hidden(k1_trees_4(k4_tarski(C,u1_struct_0(A))),k1_funct_1(u4_msualg_1(A,k1_msafree3(A,B)),k2_msualg_1(A,C))) ) ) ) ) ).
fof(t7_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ( m1_subset_1(A,k3_card_3(u4_msualg_1(B,k11_msafree(B,C))))
<=> m1_dtconstr(A,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) ) ) ).
fof(t8_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( r2_hidden(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C))
<=> k7_msaterm(A,B,D) = C ) ) ) ) ) ).
fof(t9_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k1_msafree3(A,B))))
=> m1_dtconstr(C,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0)))))),k1_msaterm(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))))) ) ) ) ).
fof(d4_msafree3,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C) )
=> k3_msafree3(A,B,C) = k3_pboole(u1_struct_0(A),B,k2_msafree3(A,C)) ) ) ) ).
fof(t11_msafree3,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B,C] :
( ( r2_hidden(B,u1_struct_0(A))
=> k1_funct_1(k2_msafree3(A,k1_trees_4(k4_tarski(C,B))),B) = k1_tarski(C) )
& ! [D] :
( ~ ( D = B
& r2_hidden(B,u1_struct_0(A)) )
=> k1_funct_1(k2_msafree3(A,k1_trees_4(k4_tarski(C,B))),D) = k1_xboole_0 ) ) ) ).
fof(t12_msafree3,axiom,
! [A,B,C] :
( l1_msualg_1(C)
=> ! [D] :
( r2_hidden(D,u1_struct_0(C))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E)
& v6_trees_3(E) )
=> ( r2_hidden(A,k1_funct_1(k2_msafree3(C,k4_trees_4(k4_tarski(B,u1_struct_0(C)),E)),D))
<=> ? [F] :
( v1_relat_1(F)
& v1_funct_1(F)
& v3_trees_2(F)
& r2_hidden(F,k2_relat_1(E))
& r2_hidden(A,k1_funct_1(k2_msafree3(C,F),D)) ) ) ) ) ) ).
fof(t13_msafree3,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C,D] :
( ( r2_hidden(D,k1_funct_1(B,C))
=> k1_funct_1(k3_msafree3(A,B,k1_trees_4(k4_tarski(D,C))),C) = k1_tarski(D) )
& ! [E] :
( ~ ( E = C
& r2_hidden(D,k1_funct_1(B,C)) )
=> k1_funct_1(k3_msafree3(A,B,k1_trees_4(k4_tarski(D,C))),E) = k1_xboole_0 ) ) ) ) ).
fof(t14_msafree3,axiom,
! [A,B,C] :
( l1_msualg_1(C)
=> ! [D] :
( m1_pboole(D,u1_struct_0(C))
=> ! [E] :
( r2_hidden(E,u1_struct_0(C))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F)
& v6_trees_3(F) )
=> ( r2_hidden(A,k1_funct_1(k3_msafree3(C,D,k4_trees_4(k4_tarski(B,u1_struct_0(C)),F)),E))
<=> ? [G] :
( v1_relat_1(G)
& v1_funct_1(G)
& v3_trees_2(G)
& r2_hidden(G,k2_relat_1(F))
& r2_hidden(A,k1_funct_1(k3_msafree3(C,D,G),E)) ) ) ) ) ) ) ).
fof(t15_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> r2_pboole(u1_struct_0(A),k2_msafree3(A,C),B) ) ) ) ).
fof(d5_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> k4_msafree3(A,B,C) = k2_msafree3(A,C) ) ) ) ).
fof(t16_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> r6_pboole(u1_struct_0(A),k4_msafree3(A,B,C),k3_msafree3(A,B,C)) ) ) ) ).
fof(t17_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( m1_pboole(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(A,k1_funct_1(k5_msafree3(B,C,D),E))
=> m1_dtconstr(A,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) ) ) ) ) ).
fof(t18_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(D,k1_funct_1(k5_msafree3(A,B,C),E))
=> ( k7_msaterm(A,B,D) = E
& r2_pboole(u1_struct_0(A),k4_msafree3(A,B,D),C) ) ) ) ) ) ) ) ).
fof(t19_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( m1_pboole(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(k1_trees_4(k4_tarski(A,E)),k1_funct_1(k5_msafree3(B,C,D),E))
<=> ( r2_hidden(A,k1_funct_1(D,E))
& r2_hidden(A,k1_funct_1(C,E)) ) ) ) ) ) ) ).
fof(t20_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_msaterm(E,A,B,k2_msaterm(A,B,D))
=> ( r2_hidden(k6_msaterm(A,B,k2_msaterm(A,B,D),E),k1_funct_1(k5_msafree3(A,B,C),k2_msualg_1(A,D)))
<=> r1_tarski(k5_relset_1(k5_numbers,k5_trees_3(u1_struct_0(k5_msafree(A,B))),E),k3_card_3(k5_msafree3(A,B,C))) ) ) ) ) ) ) ).
fof(t21_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B)))
=> ( v3_msualg_2(C,A,k11_msafree(A,B))
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_msaterm(E,A,B,k2_msaterm(A,B,D))
=> ( r1_tarski(k5_relset_1(k5_numbers,k5_trees_3(u1_struct_0(k5_msafree(A,B))),E),k3_card_3(C))
=> r2_hidden(k6_msaterm(A,B,k2_msaterm(A,B,D),E),k1_funct_1(C,k2_msualg_1(A,D))) ) ) ) ) ) ) ) ).
fof(t22_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> v3_msualg_2(k5_msafree3(A,B,C),A,k11_msafree(A,B)) ) ) ) ).
fof(t23_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> r2_pboole(u1_struct_0(A),k1_equation(u1_struct_0(A),C,k15_msafree(A,B)),k5_msafree3(A,B,C)) ) ) ) ).
fof(t24_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0)))))),k1_msaterm(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0)))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(k5_msafree3(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))),B),D))
=> r2_hidden(C,k1_funct_1(u4_msualg_1(A,k1_msafree3(A,B)),D)) ) ) ) ) ) ).
fof(t25_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,k1_msafree3(A,B)),k5_msafree3(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))),B)) ) ) ).
fof(t26_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> k10_msualg_2(A,k11_msafree(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0)))),k5_msafree3(A,k2_pboole(u1_struct_0(A),B,k2_pre_circ(u1_struct_0(A),k6_domain_1(k5_numbers,np__0))),B)) = k1_msafree3(A,B) ) ) ).
fof(t27_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_msualg_2(D,A,k11_msafree(A,B))
=> ! [E] :
( m1_msualg_2(E,A,k11_msafree(A,C))
=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
=> g3_msualg_1(A,u4_msualg_1(A,D),u5_msualg_1(A,D)) = g3_msualg_1(A,u4_msualg_1(A,E),u5_msualg_1(A,E)) ) ) ) ) ) ) ).
fof(t28_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k3_card_3(u4_msualg_1(A,k1_msafree3(A,B))))
=> r2_pboole(u1_struct_0(A),k2_msafree3(A,D),B) ) ) ) ) ).
fof(t29_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> r2_pboole(u1_struct_0(A),k4_msafree3(A,B,C),B) ) ) ) ).
fof(t30_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C))
=> ( D = E
=> k7_msaterm(A,B,D) = k7_msaterm(A,C,E) ) ) ) ) ) ) ).
fof(t31_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C))
=> ( r2_pboole(u1_struct_0(A),k4_msafree3(A,C,D),B)
=> m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ) ).
fof(t32_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> k1_msafree3(A,B) = k11_msafree(A,B) ) ) ).
fof(t33_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_trees_1(D,k1_relat_1(C))
=> r2_pboole(u1_struct_0(A),k4_msafree3(A,B,k8_msaterm(A,B,C,D)),k4_msafree3(A,B,C)) ) ) ) ) ).
fof(t34_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k1_msafree3(A,B))))
=> ! [D] :
( m1_trees_1(D,k1_relat_1(C))
=> m1_subset_1(k5_trees_2(C,D),k3_card_3(u4_msualg_1(A,k1_msafree3(A,B)))) ) ) ) ) ).
fof(t35_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_subset_1(D,k2_relat_1(C))
=> D = k4_tarski(k1_mcart_1(D),k2_mcart_1(D)) ) ) ) ) ).
fof(t36_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k3_card_3(u4_msualg_1(B,k1_msafree3(B,C))))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( ( r2_hidden(A,k1_funct_1(k2_msafree3(B,D),E))
=> r2_hidden(k4_tarski(A,E),k2_relat_1(D)) )
& ( r2_hidden(k4_tarski(A,E),k2_relat_1(D))
=> ( r2_hidden(A,k1_funct_1(k2_msafree3(B,D),E))
& r2_hidden(A,k1_funct_1(C,E)) ) ) ) ) ) ) ) ).
fof(t37_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_funct_1(B,C) = k1_xboole_0
& ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ~ ( k2_msualg_1(A,D) = C
& k1_msualg_1(A,D) = k1_xboole_0 ) ) ) )
=> v5_msualg_1(k1_msafree3(A,B),A) ) ) ) ).
fof(t38_msafree3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> r1_tarski(k3_msualg_1(A,D,C),k3_msualg_1(A,D,B)) ) ) ) ) ).
fof(t39_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_msualg_6(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_2(C,A,B)
=> v1_msualg_6(C,A) ) ) ) ).
fof(t40_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ( v1_msualg_6(k1_msafree3(A,B),A)
& v2_msafree(k1_msafree3(A,B),A) ) ) ) ).
fof(dt_k1_msafree3,axiom,
! [A,B] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v4_msualg_1(k1_msafree3(A,B),A)
& l3_msualg_1(k1_msafree3(A,B),A) ) ) ).
fof(dt_k2_msafree3,axiom,
! [A,B] :
( ( l1_msualg_1(A)
& ~ v1_xboole_0(B)
& v1_relat_1(B) )
=> m1_pboole(k2_msafree3(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_msafree3,axiom,
! [A,B,C] :
( ( l1_msualg_1(A)
& m1_pboole(B,u1_struct_0(A))
& ~ v1_xboole_0(C)
& v1_relat_1(C) )
=> m4_pboole(k3_msafree3(A,B,C),u1_struct_0(A),B) ) ).
fof(dt_k4_msafree3,axiom,
! [A,B,C] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k1_msaterm(A,B)) )
=> m4_pboole(k4_msafree3(A,B,C),u1_struct_0(A),B) ) ).
fof(dt_k5_msafree3,axiom,
! [A,B,C] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_pboole(C,u1_struct_0(A)) )
=> m4_pboole(k5_msafree3(A,B,C),u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B))) ) ).
fof(d3_msafree3,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ( C = k2_msafree3(A,B)
<=> ! [D] :
( r2_hidden(D,u1_struct_0(A))
=> k1_funct_1(C,D) = a_2_0_msafree3(B,D) ) ) ) ) ) ).
fof(t10_msafree3,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C) )
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),B)
=> ( r6_pboole(u1_struct_0(A),D,k3_msafree3(A,B,C))
<=> ! [E] :
( r2_hidden(E,u1_struct_0(A))
=> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),a_2_0_msafree3(C,E)) ) ) ) ) ) ) ).
fof(d6_msafree3,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B)))
=> ( D = k5_msafree3(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(D,E) = a_4_0_msafree3(A,B,C,E) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_msafree3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B) )
=> ( r2_hidden(A,a_2_0_msafree3(B,C))
<=> ? [D] :
( m1_subset_1(D,k2_relat_1(B))
& A = k1_mcart_1(D)
& k2_mcart_1(D) = C ) ) ) ).
fof(fraenkel_a_4_0_msafree3,axiom,
! [A,B,C,D,E] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& m1_pboole(D,u1_struct_0(B))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_0_msafree3(B,C,D,E))
<=> ? [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C))
& A = F
& k7_msaterm(B,C,F) = E
& r2_pboole(u1_struct_0(B),k4_msafree3(B,C,F),D) ) ) ) ).
%------------------------------------------------------------------------------